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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 73, 2018 - Issue 3
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Original Articles

A case study of a time step validation strategy and convergence method for oscillatory numerical simulation of a heat transfer process

, , , &
Pages 195-208 | Received 29 Sep 2017, Accepted 20 Dec 2017, Published online: 16 Jan 2018
 

ABSTRACT

A convergence identification method for oscillatory numerical simulation is proposed, in which the numerical solution can converge at the inflection point with respect to the time step. In addition, an algorithm to verify the appropriate time step is also proposed. The feasibility of the proposed method is further verified by its application to a case study involving combined natural and magnetohydrodynamics convection in a Joule-heated cavity using finite-volume methods. It is found that the two approaches have the same results and can judge the validity of the time step used in accurate computation of fluid flow and heat transfer.

Nomenclature

A=

amplitude

g=

gravitational acceleration (m/s2)

Ha=

Hartmann number

L=

enclosure height (m)

Pr=

Prandtl number

Ra=

Rayleigh number

t=

period, time (s)

T=

temperature (K)

u=

x-velocity component (m/s)

U=

dimensionless x-velocity component

v=

y-velocity component (m/s)

V=

dimensionless y-velocity component

W=

enclosure width (m)

x=

x-coordinate (m)

X=

dimensionless x-coordinate

y=

y-coordinate (m)

Y=

dimensionless y-coordinate

Greek symbols=
θ=

dimensionless temperature

σ=

electrical conductivity (ms/s)

τ=

dimensionless time

φ=

potential difference (V)

Nomenclature

A=

amplitude

g=

gravitational acceleration (m/s2)

Ha=

Hartmann number

L=

enclosure height (m)

Pr=

Prandtl number

Ra=

Rayleigh number

t=

period, time (s)

T=

temperature (K)

u=

x-velocity component (m/s)

U=

dimensionless x-velocity component

v=

y-velocity component (m/s)

V=

dimensionless y-velocity component

W=

enclosure width (m)

x=

x-coordinate (m)

X=

dimensionless x-coordinate

y=

y-coordinate (m)

Y=

dimensionless y-coordinate

Greek symbols=
θ=

dimensionless temperature

σ=

electrical conductivity (ms/s)

τ=

dimensionless time

φ=

potential difference (V)

Additional information

Funding

This work is supported by the National Science Foundations of China (51176132).

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